Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x-5y &= 3 \\ -9x+3y &= 3\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = 9x+3$ Divide both sides by $3$ to isolate $y$ $y = {3x + 1}$ Substitute this expression for $y$ in the first equation. $7x-5({3x + 1}) = 3$ $7x - 15x - 5 = 3$ Simplify by combining terms, then solve for $x$ $-8x - 5 = 3$ $-8x = 8$ $x = -1$ Substitute $-1$ for $x$ back into the top equation. $7( -1)-5y = 3$ $-7-5y = 3$ $-5y = 10$ $y = -2$ The solution is $\enspace x = -1, \enspace y = -2$.